Discussion of The Classic Magnetic Motor.

It's interesting how an idea evolves. The figure to the right shows
Chris Cheng's drawing of his idea in a simple form. The N pole
at the center was doing nothing useful. The cylindrical shield is
attached to the S pole so that the S pole "sees" through a window
in the shield, seeing N poles a bit "ahead" so the attractive
force has a forward component on the rotor. Chris' diagram also
showed N poles on the outside, without explicitly showing the S
poles of those magnets. No one has ever made magnetic monopoles,
so we must decide how to arrange the magnets so that those S poles
don't degrade the engine's performance.

In order to make use of both poles of the magnet inside the shield,
I introduced a shield with two windows (color picture).
You can easily imagine other ways to accomplish this.
This is the version posted as a puzzle on my web page.

Many PM inventors these days are tinkering with magnets on wheels.
Why the fascination with magnetism? I think it's because most people,
even those who have had physics and engineering courses, still
are a bit mystified by how magnets work, so they are less likely to
see flaws in a magnetic engine design. One such inventor tried to
convince me that magnets have unlimited stored energy, or can tap
unlimited energy from "somewhere". "Just look at those magnets on
your refrigerator," he said. "They support themselves, doing work
against the force of gravity forever, so they must
have infinite energy capability."
This is a simple misunderstanding of force and work.
A force must move an object to do work on it.
The refrigerator magnet's force doesn't move anything,
and it does no work on anything. [4]

This particular magnetic engine puzzle has been attracting a lot
of attention lately from people who say they had similar ideas.
Some folks complain to me that no solution was posted for a long time.
Others, mostly
physicists and engineers, wax eloquently about field theory, and
seem to me to be missing the point of the exercise.

Many PM proposals have multiple flaws. You might say that they can
fail on many levels. They have multiple failure modes. Some defects
can be corrected by better engineering. Just as we allow one to
assume that friction is absent, in order to expose more fundamental
flaws, we can also, one by one, correct minor flaws by better
engineering until one serious and unsurmountable one remains.

In this engine, some correspondents have pointed out minor problems:

The field due to the symmetric array of
outer magnets will be zero at the center of the array.
However, the rotating magnet poles are not at the center. Besides,
these poles are supposedly shielded from the effect of most of the outer magnets.

The rotating magnet can "see" both N and S poles of the outer array,
through the shield windows. Granted, the N poles dominate, being closer, but the system seems somewhat inefficient.

The finite array of outer magnets produces a field which varies in
strength with rotation angle. The rotating assembly might simply find a
position of relative equilibrium and just sit there, like a wheel in a
roadway rut. OK, so we put more magnets in the outer array to even out
the field. Actually this isn't a problem, for if we give the rotor
enough initial speed, it rides over the field irregularities.

The idea of magnetic shields acting like light shields (simply
blocking the field lines) is too simplistic. That's true. See below.

To meet objection 2 we improve the design by repositioning the magnets,
adding another rotating assembly on the same shaft, and shielding the magnets in each rotor from "seeing" any poles of the wrong polarity.

The second rotor must be oriented on the shaft so that the forces on it tend to rotate the shaft in the same direction as the first rotor rotates.
(IF it rotates!) We can even position the second rotor on the shaft in such a way as to smooth out the "bumpy" effects of the fields. See what a bit of engineering redesign can do? [Constructing this diagram was difficult enough. Don't expect me to explicitly show the supporting frame, shaft support, and the means for transfering the shaft rotation to something else to do useful work.]

Objection 4 is a serious one, we admit. However, in our usual spirit of
fairness to inventors, let's grant that somehow we invent a shield
that does act in such a simple way, blocking the influence of any
magnets that aren't in a line of sight through the shield windows. This task might be every bit as difficult as building a PM machine of any kind. But by granting this concession, and temporarily setting aside the problem of making such a shield, we may expose other fundamental problems with this design.

The short answer.

First, lets look at the field produced by a circular ring of magnet poles of the same polarity lying in a plane. Due to symmetry and the vector nature of force, their combined field at the center of the circle is zero. But what of their combined field elsewhere in the plane? The surprising result is that the combined field is very nearly zero anywhere in the plane, within the circle. [1] In fact, if the ring were a continous distribution of poles, the field would be exactly zero anywhere within the circle and in the plane of the circle. That continuous distribution is a useful model for further analysis.

The original form of the motor had magnets lying in a plane. This is equivalent to one circle of N poles and a larger circle of S poles. Each circle contributes nearly zero field anywhere within the smaller circle, so the net field from all magnets is nearly zero anywhere within the smaller circle, and in that same plane. [2]

So the rotating magnet and shield are "seeing" nearly zero field from the outer magnets. Therefore those magnets exert no force on the rotor. There's nothing to make the rotor move, whether or not it has shields attached. [3]

Broader implications.

The behavior of magnets is often fascinating to observe, as they exert force on each other, and on metallic objects. One is tempted to think that their movement is due to their "stored" magnetic energy, and if you could design a device to turn that stored energy into useful work, you'd have achieved, if not perpetual motion, at least something very useful. Such is the allure of magnets to perpetual motion seekers. Even if they understand that magnet internal energy is not being extracted, they suppose that the magnets are somehow a conduit of energy stored in the vacuum, or somewhere else.

The magnetic energy stored in a magnet is a paltry amount. It may easily be "extracted" by sharp blows to the magnet, or by heating the magnet. Such actions compromise the alignment of magnetic domains within the magnet. After you do this, the magnet isn't magnetized anymore. In the absence of such processes, the motion of magnets in a motor or generator device is not due to their stored magnetic energy. Such motions are entirely the result of the initial mechanical energy you give to the magnets when you place them in position relative to each other. (There can be a very slight demagnetization due to thermal and other stresses when the magnet is part of a motor or generator.)

You have seen those toys with magnet pendulums moving eratically in the field of stationary magnets placed underneath. The pendulum has very little friction, so the device moves for quite a long time before it comes to rest. But that motion hasn't used any of the energy stored in the magnetsnot one bit. You can pull the pendulum aside (giving it initial energy) and start it up again and it will run as long as before. You can repeat this time after time, day after day, and never extract any energy stored in the magnets. The only energy it needs is that you gave it when you initially pulled the magnet aside, and when that is used up, it stops.

These devices haven't extracted energy from unknown sources either. If you carefully measure and account for the mechanical energy you put into the system, and the mechanical energy that is dissipated into thermal energy, you find that all energy is fully accounted for. Magnet machines don't extract energy from the vacuum, the ether, the fourth dimension, or any other magical realm.

Notes:

[1] The reader is invited to devise a neat mathematical proof without explicitly using calculus. You might do this by considering a simple "pole" model of the magnet, with poles attracting or repelling according to an inverse square law. We are working in a two dimensional plane, so that simplifies things a lot. Then introduce a scalar potential, which obeys an inverse first power law. Now use a geometric argument to show that the scalar potential is constant anywhere within and in the plane of a circle of poles. Therefore the force derived from this potential must be zero anywhere in this plane and within the circle.

[2] If the "nearly" zero bothers you, you may argue that the field, though small, actually has a periodic variation in strength with angle, having M periods in 360° if there are M magnets. This does not help the cause of perpetual motion. If you gave the rotor a spin, pushing strongly enough, it would move with a varying speed with that same periodic variation, until frictional forces brought it to rest at one of the M positions of force equilibrium. This is the behavior one observes when attempting to make a magnet motor perpetual motion machine. Perpetual motion believers call these "sticking points", and imagine that if sticky points could be eliminated by redesign, they'd achieve perpetual motion or even over-unity performance.

[3] Using different language, the potential energy of the rotor with respect to the stator magnets has periodic variation around the circle. The rotor will come to rest at a position of relative minimum potential energy. To move it out of such a "potential well" requires exerting a force sufficient to give it additional energy equal to that of the nearby potential peak. But this is just good old energy conservation at work.

The magnetic shield turns out to be a distractor, of no importance in this device. Most respondents have gone to great lengths to argue that the perfect magnetic shield is itself an impossible device, or to postulate how a shield distorts magnetic fields, without realizing that the shield is completely irrelevant to this version of the device. [5]

Check the Annex gallery of the
Museum for a non-shielded magnet motor with a different method of
deception.

[4] Apparently this misconception is more pervasive than I thought. I seldom read internet forums and discussion groups because too many people there waste everyone's time with unfounded opinions, or by pontificating nonsense about physics as if they really understood it. A correspondent pointed me to one such instance where someone confidently declared that my comment about the refrigerator magnet was wrong:

There is [sic] a few things wrong here. One is something that was said by the person who created the site.

QUOTE: A force must move an object to do work on it. The refrigerator magnet's force doesn't move anything, and it does no work.

The magnet IS doing work by holding itself up. Say we had a metal room (ferrous metal). You could attach a permanent magnet to the ceiling and it would stay there. According to the person who made that site the magnet isn't doing work because nothing is moving? Go to a chin up bar and hang there by your arms. Don't move, just hang. Tell me your [sic] not doing work and your [sic] delusional. The magnetic motor they show there would not work I will say that but not for the reasons they give. Remove the shield and curve the magnet. Place the curved magnet on the outside in a fixed position and have the other magnets on the shaft. Oh, wait... That would be Howard Johnson's permanent magnetic motor.

In physics, the definition of work is this: "Work done by a force acting on a body is the product of the size of that force multiplied by the distance the body moves, multiplied by the cosine of the angle between the force and the distance." [Both force and distance are vectors.] Or, W = F x cos θ. (x is the distance the body moves. θ is the angle between the vectos F and x.) So, no motion, no distance moved, zero work. The clueless soul, who is so certain that I am wrong, cites the example of a person hanging from a bar, supporting his own weight. This person is certainly expending energy in this process, since muscular effort involves muscle fibres contracting and relaxing, doing microscopic scale work within the body. This work is dissipated as heat. But he does no macroscopic work on the bar or anything else outside of his body. If he were condemned to be hung by a noose until dead, his lifeless body would hang there just as well, doing no work at all.

Our refrigerator magnet is likewise doing no work, niether external nor internal, as it remains at rest firmly in place and unmoving, on the refrigerator wall, supporting its own weight.

This is just another example, of many, that shows that misunderstanding of basic, elementary, physics is the fuel that motivates perpetual motionists. Most of these folks are unable to do force and torque analysis of systems using free-body diagrams, skills that are supposed to be learned in the first half of the first semester of an elementary physics course.

[5] Dec 2007. Jacob Bayless, an engineering student at the University of British Columbia, wanted to return to the question we shelved, the magnetic shield. He points out that the magnetic shield isn't entirely irrelevant to this device. He sends a nice animated GIF showing a very simple perpetual motion machine that embodies the simplest application of the idea, stripped of the complications caused by so many magnets. Jacob's device can't be dismissed without analyzing forces on the shields. I have noticed that the most original and ingenious designs are sent to me by people who know darn well that they can't work, and know why. They are just having creative fun by imagining overcoming the impossibilities of physics.

The rotating magnet has shielding (shown in dark gray) with open apertures near each pole. The geometry allows this magnet to interact with the N pole of the stationary magnet at the lower right.
The blue arrows show when the attraction or repulsion is greatest.
Just give the rotor a push and it will turn forever!

Note that the shield apertures have different size and shape for the N and S poles. A subtle point, but indicative of good engineering design. It ensures maximum torque on the rotating system. (!)

The clinker is that field shields are never "magical" in their operation. They still must obey Newton's third law, which ensures that when a shield is acted upon by forces due other parts of the system, then the shield in turn exerts equal size and oppositely directed forces on those parts of the system. Perpetual motion machine designers seldom even consider Newton's third law, yet it is the law of nature that dooms their efforts.

[Jan 2009] I like to leave some unanswered questions to frustrate readers. One reader informs me that the answer above isn't crystal clear. So here's more.

Note that Jacob does not include the times when the stationary magnet's S pole is "seen" through one of the shield windows, and in those cases the forces retard the supposed motion of the wheel. Granted, due to the additional distance, these are somewhat weaker than the ones that flash on the screen in blue. Also, no forces are indicated during the majority of time when the windows are not aimed at a stationary pole. But there are still forces of attraction and repulsion during that time, mostly repulsion. Magnetic shields don't "beam" fields like the beam of a flashlight. The fields spread out. In fact there's strong field lines all the time from N to S pole of the rotating magnet. And, it turns out, the forces due to the fringing field are mostly such as to retard any motion of the rotor. Of course, this description assumes that there is rotational motion. There may be, for short duration, but the rotor will quickly find a position of stable equilibrium and stop there.

And, finally. If the shield is effective in modifying the field of the rotating magnet, it does so by creating a field of its own in response to the field from the small magnet (Newton's third law), and this field of the shield is opposite in size and direction (mostly) in those regions where it is effective in "canceling" the magnet's field. Now if it does that, than it must also be doing the same sort of thing for the fixed (larger) magnet at lower right. (Shields don't discriminate.) And here Lenz's law comes into play (a magnetic result of Newton's third), such that the motion of the magnetic shield is opposed by the larger magnet. On my physics demo page I have a Lenz law demo that involves dropping a strong magnet down an aluminum tube. When this is done, the moving field of the magnet induces current in the aluminum which has fields which oppose the change in motion of the magnet. So this decreases the magnet's downward acceleration, and it quickly reaches a slow terminal velocity and arrives at the bottom of the tube much later than if it were in free fall the same distance.

I was hoping some computer whiz with access to software that models magnetic fields dynamically might run this through the computer and see what results. Quite a few perpetual motion enthusiasts have done this for their own inventions, and report that their idea "shows promise". But none took the bait and modeled this one. The software that I've seen which does such simulations usually has propagating computational errors that can fool you into thinking there's a "slight tendency to sustain rotational motion". Very slight. Besides, this software is not designed to calculate forces on a magnetic shield.

That's when the software is set up properly. But usually these people don't set it up right, and omit some "little detail" that they didn't think important.

Here we need to remind ourselves, yet again, that there is no known perfect magnetic shield for static or quasi-static magnetic fields. But even if we allow such a perfect shield for the sake of analysis (just as we allow frictionless bearings), these magnetic motors using shields would not have over-unity performance.